Boolean data type

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Boolean_data_type 

In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean condition evaluates to true or false. It is a special case of a more general logical data type—logic does not always need to be Boolean (see probabilistic logic).

Generalities

In programming languages with a built-in Boolean data type, such as Pascal and Java, the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions.

Languages with no explicit Boolean data type, like C90 and Lisp, may still represent truth values by some other data type. Common Lisp uses an empty list for false, and any other value for true. The C programming language uses an integer type, where relational expressions like i > j and logical expressions connected by && and || are defined to have value 1 if true and 0 if false, whereas the test parts of if, while, for, etc., treat any non-zero value as true. Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (bit), or as a bit string of length one, which can store only two values. The implementation of Booleans in computers are most likely represented as a full word, rather than a bit; this is usually due to the ways computers transfer blocks of information.

Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=, ¬), and negation (NOT, ~, !, ¬).

In some languages, like Ruby, Smalltalk, and Alice the true and false values belong to separate classes, e.g., True and False, respectively, so there is no one Boolean type.

In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls, the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can be restricted to just TRUE and FALSE though.

Language-specific implementations

ALGOL and the built-in BOOLEAN type

One of the earliest programming languages to provide an explicit BOOLEAN data type is ALGOL 60 (1960) with values true and false and logical operators denoted by symbols '${\displaystyle \wedge }$' (and), '${\displaystyle \vee }$' (or), '${\displaystyle \supset }$' (implies), '${\displaystyle \equiv }$' (equivalence), and '${\displaystyle \mathrm{\neg }}$' (not). Due to input device and character set limits on many computers of the time, however, most compilers used alternative representations for many of the operators, such as AND or 'AND'.

This approach with BOOLEAN as a built-in (either primitive or otherwise predefined) data type was adopted by many later programming languages, such as Simula 67 (1967), ALGOL 68 (1970), Pascal (1970), Ada (1980), Java (1995), and C# (2000), among others.

Fortran

The first version of FORTRAN (1957) and its successor FORTRAN II (1958) have no logical values or operations; even the conditional IF statement takes an arithmetic expression and branches to one of three locations according to its sign; see arithmetic IF. FORTRAN IV (1962), however, follows the ALGOL 60 example by providing a Boolean data type (LOGICAL), truth literals (.TRUE. and .FALSE.), Boolean-valued numeric comparison operators (.EQ., .GT., etc.), and logical operators (.NOT., .AND., .OR.). In FORMAT statements, a specific format descriptor ('L') is provided for the parsing or formatting of logical values.

Lisp and Scheme

The language Lisp (1958) never had a built-in Boolean data type. Instead, conditional constructs like cond assume that the logical value false is represented by the empty list (), which is defined to be the same as the special atom nil or NIL; whereas any other s-expression is interpreted as true. For convenience, most modern dialects of Lisp predefine the atom t to have value t, so that t can be used as a mnemonic notation for true.

This approach (any value can be used as a Boolean value) was retained in most Lisp dialects (Common Lisp, Scheme, Emacs Lisp), and similar models were adopted by many scripting languages, even ones having a distinct Boolean type or Boolean values; although which values are interpreted as false and which are true vary from language to language. In Scheme, for example, the false value is an atom distinct from the empty list, so the latter is interpreted as true. Common Lisp, on the other hand, also provides the dedicated boolean type, derived as a specialization of the symbol.

Pascal, Ada, and Haskell

The language Pascal (1970) popularized the concept of programmer-defined enumerated types, previously available with different nomenclature in COBOL, FACT and JOVIAL. A built-in Boolean data type was then provided as a predefined enumerated type with values FALSE and TRUE. By definition, all comparisons, logical operations, and conditional statements applied to and/or yielded Boolean values. Otherwise, the Boolean type had all the facilities which were available for enumerated types in general, such as ordering and use as indices. In contrast, converting between Booleans and integers (or any other types) still required explicit tests or function calls, as in ALGOL 60. This approach (Boolean is an enumerated type) was adopted by most later languages which had enumerated types, such as Modula, Ada, and Haskell.

C, C++, Objective-C, AWK

Initial implementations of the language C (1972) provided no Boolean type, and to this day Boolean values are commonly represented by integers (ints) in C programs. The comparison operators (>, ==, etc.) are defined to return a signed integer (int) result, either 0 (for false) or 1 (for true). Logical operators (&&, ||, !, etc.) and condition-testing statements (if, while) assume that zero is false and all other values are true.

After enumerated types (enums) were added to the American National Standards Institute version of C, ANSI C (1989), many C programmers got used to defining their own Boolean types as such, for readability reasons. However, enumerated types are equivalent to integers according to the language standards; so the effective identity between Booleans and integers is still valid for C programs.

Standard C (since C99) provides a Boolean type, called _Bool. By including the header stdbool.h, one can use the more intuitive name bool and the constants true and false. The language guarantees that any two true values will compare equal (which was impossible to achieve before the introduction of the type). Boolean values still behave as integers, can be stored in integer variables, and used anywhere integers would be valid, including in indexing, arithmetic, parsing, and formatting. This approach (Boolean values are just integers) has been retained in all later versions of C. Note, that this does not mean that any integer value can be stored in a Boolean variable.

C++ has a separate Boolean data type bool, but with automatic conversions from scalar and pointer values that are very similar to those of C. This approach was adopted also by many later languages, especially by some scripting languages such as AWK.

Objective-C also has a separate Boolean data type BOOL, with possible values being YES or NO, equivalents of true and false respectively. Also, in Objective-C compilers that support C99, C's _Bool type can be used, since Objective-C is a superset of C.

Java

In Java, the value of the boolean data type can only be either true or false.

Perl and Lua

Perl has no Boolean data type. Instead, any value can behave as Boolean in Boolean context (condition of if or while statement, argument of && or ||, etc.). The number 0, the strings "0" and "", the empty list (), and the special value undef evaluate to false. All else evaluates to true.

Lua has a Boolean data type, but non-Boolean values can also behave as Booleans. The non-value nil evaluates to false, whereas every other data type value evaluates to true. This includes the empty string "" and the number 0, which are very often considered false in other languages.

PL/I

PL/I has no Boolean data type. Instead, comparison operators generate BIT(1) values; '0'B represents false and '1'B represents true. The operands of, e.g., &, |, ¬, are converted to bit strings and the operations are performed on each bit. The element-expression of an IF statement is true if any bit is 1.

Rexx

Rexx has no Boolean data type. Instead, comparison operators generate 0 or 1; 0 represents false and 1 represents true. The operands of, e.g., &, |, ¬, must be 0 or 1.

Tcl

Tcl has no separate Boolean type. Like in C, the integers 0 (false) and 1 (true—in fact any nonzero integer) are used.

Examples of coding:

 set v 1
 if { $v } { puts "V is 1 or true" }

The above will show V is 1 or true since the expression evaluates to 1.

 set v ""
 if { $v } ....

The above will render an error, as variable v cannot be evaluated as 0 or 1.

Python, Ruby, and JavaScript

Python, from version 2.3 forward, has a bool type which is a subclass of int, the standard integer type. It has two possible values: True and False, which are special versions of 1 and 0 respectively and behave as such in arithmetic contexts. Also, a numeric value of zero (integer or fractional), the null value (None), the empty string, and empty containers (lists, sets, etc.) are considered Boolean false; all other values are considered Boolean true by default. Classes can define how their instances are treated in a Boolean context through the special method __nonzero__ (Python 2) or __bool__ (Python 3). For containers, __len__ (the special method for determining the length of containers) is used if the explicit Boolean conversion method is not defined.

In Ruby, in contrast, only nil (Ruby's null value) and a special false object are false; all else (including the integer 0 and empty arrays) is true.

In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are sometimes called falsy (of which the complement is truthy) to distinguish between strictly type-checked and coerced Booleans. As opposed to Python, empty containers (Arrays, Maps, Sets) are considered truthy. Languages such as PHP also use this approach.

SQL

Main article: Null (SQL) § Comparisons with NULL and the three-valued logic (3VL)

Booleans appear in SQL when a condition is needed, such as WHERE clause, in form of predicate which is produced by using operators such as comparison operators, IN operator, IS (NOT) NULL etc. However, apart from TRUE and FALSE, these operators can also yield a third state, called UNKNOWN, when comparison with NULL is made.

The SQL92 standard introduced IS (NOT) TRUE, IS (NOT) FALSE, and IS (NOT) UNKNOWN operators which evaluate a predicate, which predated the introduction of Boolean type in SQL:1999.

The SQL:1999 standard introduced a BOOLEAN data type as an optional feature (T031). When restricted by a NOT NULL constraint, a SQL BOOLEAN behaves like Booleans in other languages, which can store only TRUE and FALSE values. However, if it is nullable, which is the default like all other SQL data types, it can have the special null value also. Although the SQL standard defines three literals for the BOOLEAN type – TRUE, FALSE, and UNKNOWN — it also says that the NULL BOOLEAN and UNKNOWN "may be used interchangeably to mean exactly the same thing". This has caused some controversy because the identification subjects UNKNOWN to the equality comparison rules for NULL. More precisely UNKNOWN = UNKNOWN is not TRUE but UNKNOWN/NULL. As of 2012 few major SQL systems implement the T031 feature. Firebird and PostgreSQL are notable exceptions, although PostgreSQL implements no UNKNOWN literal; NULL can be used instead.

The treatment of Boolean values differs between SQL systems.

For example, in Microsoft SQL Server, Boolean value is not supported at all, neither as a standalone data type nor representable as an integer. It shows the error message "An expression of non-Boolean type specified in a context where a condition is expected" if a column is directly used in the WHERE clause, e.g. SELECT a FROM t WHERE a, while a statement such as SELECT column IS NOT NULL FROM t yields a syntax error. The BIT data type, which can only store integers 0 and 1 apart from NULL, is commonly used as a workaround to store Boolean values, but workarounds need to be used such as UPDATE t SET flag = IIF(col IS NOT NULL, 1, 0) WHERE flag = 0 to convert between the integer and Boolean expression.

Microsoft Access, which uses the Access Database Engine (ACE/JET), also does not have a Boolean data type. Similar to MS SQL Server, it uses a BIT data type. In Access it is known as a Yes/No data type which can have two values; Yes (True) or No (False). The BIT data type in Access can also can be represented numerically; True is −1 and False is 0. This differs to MS SQL Server in two ways, even though both are Microsoft products:

1. Access represents TRUE as −1, while it is 1 in SQL Server
2. Access does not support the Null tri-state, supported by SQL Server

PostgreSQL has a distinct BOOLEAN type as in the standard, which allows predicates to be stored directly into a BOOLEAN column, and allows using a BOOLEAN column directly as a predicate in a WHERE clause.

In MySQL, BOOLEAN is treated as an alias of TINYINT(1); TRUE is the same as integer 1 and FALSE is the same is integer 0. Any non-zero integer is true in conditions.

Tableau

Tableau Software has a BOOLEAN data type. The literal of a Boolean value is True or False.

The Tableau INT() function converts a Boolean to a number, returning 1 for True and 0 for False.

Forth

Forth (programming language) has no Boolean type, it uses regular integers: value 0 (all bits low) represents false, and -1 (all bits high) represents true. This allows the language to define only one set of logical operators, instead of one for mathematical calculations and one for conditions.

Material conditional

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Material_conditional

The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol ${\displaystyle \to }$ is interpreted as material implication, a formula ${\displaystyle P\to Q}$ is true unless ${\displaystyle P}$ is true and ${\displaystyle Q}$ is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.

Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language.

Notation

In logic and related fields, the material conditional is customarily notated with an infix operator ${\displaystyle \to }$. The material conditional is also notated using the infixes ${\displaystyle \supset }$ and ${\displaystyle \Rightarrow }$. In the prefixed Polish notation, conditionals are notated as ${\displaystyle Cpq}$. In a conditional formula ${\displaystyle p\to q}$, the subformula ${\displaystyle p}$ is referred to as the antecedent and ${\displaystyle q}$ is termed the consequent of the conditional. Conditional statements may be nested such that the antecedent or the consequent may themselves be conditional statements, as in the formula ${\displaystyle (p\to q)\to (r\to s)}$.

History

In Arithmetices Principia: Nova Methodo Exposita (1889), Peano expressed the proposition "If ${\displaystyle A}$ then ${\displaystyle B}$" as ${\displaystyle A}$ Ɔ ${\displaystyle B}$ with the symbol Ɔ, which is the opposite of C. He also expressed the proposition ${\displaystyle A\supset B}$ as ${\displaystyle A}$ Ɔ ${\displaystyle B}$. Hilbert expressed the proposition "If A then B" as ${\displaystyle A\to B}$ in 1918. Russell followed Peano in his Principia Mathematica (1910–1913), in which he expressed the proposition "If A then B" as ${\displaystyle A\supset B}$. Following Russell, Gentzen expressed the proposition "If A then B" as ${\displaystyle A\supset B}$. Heyting expressed the proposition "If A then B" as ${\displaystyle A\supset B}$ at first but later came to express it as ${\displaystyle A\to B}$ with a right-pointing arrow. Bourbaki expressed the proposition "If A then B" as ${\displaystyle A\Rightarrow B}$ in 1954.

Definitions

Semantics

From a semantic perspective, material implication is the binary truth functional operator which returns "true" unless its first argument is true and its second argument is false. This semantics can be shown graphically in a truth table such as the one below.

Truth table

The truth table of p → q:

${\displaystyle p}$	${\displaystyle q}$	${\displaystyle p}$ → ${\displaystyle q}$
True	True	True
True	False	False
False	True	True
False	False	True

The third and fourth logical cases of this truth table, where the antecedent p is false and p → q is true, are called "vacuous truths".

Deductive definition

Material implication can also be characterized deductively in terms of the following rules of inference.

• Modus ponens
• Conditional proof
• Classical contraposition
• Classical reductio ad absurdum

Unlike the semantic definition, this approach to logical connectives permits the examination of structurally identical propositional forms in various logical systems, where somewhat different properties may be demonstrated. For example, in intuitionistic logic, which rejects proofs by contraposition as valid rules of inference, (p → q) ⇒ ¬p ∨ q is not a propositional theorem, but the material conditional is used to define negation.

Formal properties

When disjunction, conjunction and negation are classical, material implication validates the following equivalences:

• Contraposition: ${\displaystyle P\to Q\equiv \mathrm{\neg }Q\to \mathrm{\neg }P}$
• Import-export: ${\displaystyle P\to (Q\to R)\equiv (P\wedge Q)\to R}$
• Negated conditionals: ${\displaystyle \mathrm{\neg }(P\to Q)\equiv P\wedge \mathrm{\neg }Q}$
• Or-and-if: ${\displaystyle P\to Q\equiv \mathrm{\neg }P\vee Q}$
• Commutativity of antecedents: ${\displaystyle (P\to (Q\to R))\equiv (Q\to (P\to R))}$
• Distributivity: ${\displaystyle (R\to (P\to Q))\equiv ((R\to P)\to (R\to Q))}$

Similarly, on classical interpretations of the other connectives, material implication validates the following entailments:

• Antecedent strengthening: ${\displaystyle P\to Q\models (P\wedge R)\to Q}$
• Vacuous conditional: ${\displaystyle \mathrm{\neg }P\models P\to Q}$
• Transitivity: ${\displaystyle (P\to Q)\wedge (Q\to R)\models P\to R}$
• Simplification of disjunctive antecedents: ${\displaystyle (P\vee Q)\to R\models (P\to R)\wedge (Q\to R)}$

Tautologies involving material implication include:

• Reflexivity: ${\displaystyle \models P\to P}$
• Totality: ${\displaystyle \models (P\to Q)\vee (Q\to P)}$
• Conditional excluded middle: ${\displaystyle \models (P\to Q)\vee (P\to \mathrm{\neg }Q)}$

Discrepancies with natural language

Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is itself true, but speakers typically reject sentences such as "If I have a penny in my pocket, then Paris is in France". These classic problems have been called the paradoxes of material implication. In addition to the paradoxes, a variety of other arguments have been given against a material implication analysis. For instance, counterfactual conditionals would all be vacuously true on such an account.

In the mid-20th century, a number of researchers including H. P. Grice and Frank Jackson proposed that pragmatic principles could explain the discrepancies between natural language conditionals and the material conditional. On their accounts, conditionals denote material implication but end up conveying additional information when they interact with conversational norms such as Grice's maxims. Recent work in formal semantics and philosophy of language has generally eschewed material implication as an analysis for natural-language conditionals. In particular, such work has often rejected the assumption that natural-language conditionals are truth functional in the sense that the truth value of "If P, then Q" is determined solely by the truth values of P and Q. Thus semantic analyses of conditionals typically propose alternative interpretations built on foundations such as modal logic, relevance logic, probability theory, and causal models.

Similar discrepancies have been observed by psychologists studying conditional reasoning, for instance, by the notorious Wason selection task study, where less than 10% of participants reasoned according to the material conditional. Some researchers have interpreted this result as a failure of the participants to confirm to normative laws of reasoning, while others interpret the participants as reasoning normatively according to nonclassical laws.

Substantia nigra

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Substantia_nigra 

 

Substantia nigra
Substantia nigra highlighted in red.
Section through superior colliculus showing Substantia nigra.
Details
Part of	Midbrain, Basal ganglia
Identifiers
Latin	Substantia nigra
Acronym(s)	SN
MeSH	D013378
NeuroNames	536
NeuroLex ID	birnlex_789
TA98	A14.1.06.111
TA2	5881
FMA	67947

The substantia nigra (SN) is a basal ganglia structure located in the midbrain that plays an important role in reward and movement. Substantia nigra is Latin for "black substance", reflecting the fact that parts of the substantia nigra appear darker than neighboring areas due to high levels of neuromelanin in dopaminergic neurons. Parkinson's disease is characterized by the loss of dopaminergic neurons in the substantia nigra pars compacta.

Although the substantia nigra appears as a continuous band in brain sections, anatomical studies have found that it actually consists of two parts with very different connections and functions: the pars compacta (SNpc) and the pars reticulata (SNpr). The pars compacta serves mainly as a projection to the basal ganglia circuit, supplying the striatum with dopamine. The pars reticulata conveys signals from the basal ganglia to numerous other brain structures.

Structure

Coronal slices of human brain showing the basal ganglia, globus pallidus: external segment (GPe), subthalamic nucleus (STN), globus pallidus: internal segment (GPi), and substantia nigra (SN, red). The right section is the deeper one, closer to the back of the head

Diagram of the main components of the basal ganglia and their interconnections

Anatomical overview of the main circuits of the basal ganglia, substantia nigra is shown in black. Picture shows 2 coronal slices that have been superimposed to include the involved basal ganglia structures. + and – signs at the point of the arrows indicate respectively whether the pathway is excitatory or inhibitory in effect. Green arrows refer to excitatory glutamatergic pathways, red arrows refer to inhibitory GABAergic pathways and turquoise arrows refer to dopaminergic pathways that are excitatory on the direct pathway and inhibitory on the indirect pathway.

See also: Primate basal ganglia system

The substantia nigra, along with four other nuclei, is part of the basal ganglia. It is the largest nucleus in the midbrain, lying dorsal to the cerebral peduncles. Humans have two substantiae nigrae, one on each side of the midline.

The SN is divided into two parts: the pars reticulata (SNpr) and the pars compacta (SNpc), which lies medial to the pars reticulata. Sometimes, a third region, the pars lateralis, is mentioned, though it is usually classified as part of the pars reticulata. The (SNpr) and the internal globus pallidus (GPi) are separated by the internal capsule.

Pars reticulata

Main article: Pars reticulata

The pars reticulata bears a strong structural and functional resemblance to the internal part of the globus pallidus. The two are sometimes considered parts of the same structure, separated by the white matter of the internal capsule. Like those of the globus pallidus, the neurons in pars reticulata are mainly GABAergic.

Afferent connections

The main input to the SNpr derives from the striatum. It comes by two routes, known as the direct and indirect pathways. The direct pathway consists of axons from medium spiny cells in the striatum that project directly to pars reticulata. The indirect pathway consists of three links: a projection from striatal medium spiny cells to the external part of the globus pallidus; a GABAergic projection from the globus pallidus to the subthalamic nucleus, and a glutamatergic projection from the subthalamic nucleus to the pars reticulata. Thus, striatal activity via the direct pathway exerts an inhibitory effect on neurons in the (SNpr) but an excitatory effect via the indirect pathway. The direct and indirect pathways originate from different subsets of striatal medium spiny cells: They are tightly intermingled, but express different types of dopamine receptors, as well as showing other neurochemical differences.

Efferent connections

Significant projections occur to the thalamus (ventral lateral and ventral anterior nuclei), superior colliculus, and other caudal nuclei from the pars reticulata (the nigrothalamic pathway), which use GABA as their neurotransmitter. In addition, these neurons form up to five collaterals that branch within both the pars compacta and pars reticulata, likely modulating dopaminergic activity in the pars compacta.

Function

The substantia nigra is an important player in brain function, in particular, in eye movement, motor planning, reward-seeking, learning, and addiction. Many of the substantia nigra's effects are mediated through the striatum. The nigral dopaminergic input to the striatum via the nigrostriatal pathway is intimately linked with the striatum's function. The co-dependence between the striatum and substantia nigra can be seen in this way: when the substantia nigra is electrically stimulated, no movement occurs; however, the symptoms of nigral degeneration due to Parkinson's is a poignant example of the substantia nigra's influence on movement. In addition to striatum-mediated functions, the substantia nigra also serves as a major source of GABAergic inhibition to various brain targets.

Pars reticulata

Main article: Pars reticulata § Function

The pars reticulata of the substantia nigra is an important processing center in the basal ganglia. The GABAergic neurons in the pars reticulata convey the final processed signals of the basal ganglia to the thalamus and superior colliculus. In addition, the pars reticulata also inhibits dopaminergic activity in the pars compacta via axon collaterals, although the functional organization of these connections remains unclear.

The GABAergic neurons of the pars reticulata spontaneously fire action potentials. In rats, the frequency of action potentials is roughly 25 Hz. The purpose of these spontaneous action potentials is to inhibit targets of the basal ganglia, and decreases in inhibition are associated with movement. The subthalamic nucleus gives excitatory input that modulates the rate of firing of these spontaneous action potentials. However, lesion of the subthalamic nucleus leads to only a 20% decrease in pars reticulata firing rate, suggesting that the generation of action potentials in the pars reticulata is largely autonomous, as exemplified by the pars reticulata's role in saccadic eye movement. A group of GABAergic neurons from the pars reticulata projects to the superior colliculus, exhibiting a high level of sustained inhibitory activity. Projections from the caudate nucleus to the superior colliculus also modulate saccadic eye movement. Altered patterns of pars reticulata firing such as single-spike or burst firing are found in Parkinson's disease and epilepsy.

Pars compacta

Main article: Pars compacta § Function

The most prominent function of the pars compacta is motor control, though the substantia nigra's role in motor control is indirect; electrical stimulation of the substantia nigra does not result in movement, due to mediation of the striatum in the nigral influence of movement. The pars compacta sends excitatory input to the striatum via D1 pathway that excites and activates the striatum, resulting in the release of GABA onto the globus pallidus to inhibit its inhibitory effects on the thalamic nucleus. This causes the thalamocortical pathways to become excited and transmits motor neuron signals to the cerebral cortex to allow the initiation of movement, which is absent in Parkinson's disease. However, lack of pars compacta neurons has a large influence on movement, as evidenced by the symptoms of Parkinson's. The motor role of the pars compacta may involve fine motor control, as has been confirmed in animal models with lesions in that region.

The pars compacta is heavily involved in learned responses to stimuli. In primates, dopaminergic neuron activity increases in the nigrostriatal pathway when a new stimulus is presented. Dopaminergic activity decreases with repeated stimulus presentation. However, behaviorally significant stimulus presentation (i.e. rewards) continues to activate dopaminergic neurons in the substantia nigra pars compacta. Dopaminergic projections from the ventral tegmental area (bottom part of the "midbrain" or mesencephalon) to the prefrontal cortex (mesocortical pathway) and to the nucleus accumbens (mesolimbic pathway – "meso" referring to "from the mesencephalon"... specifically the ventral tegmental area) are implicated in reward, pleasure, and addictive behavior. The pars compacta is also important in spatial learning, the observations about one's environment and location in space. Lesions in the pars compacta lead to learning deficits in repeating identical movements, and some studies point to its involvement in a dorsal striatal-dependent, response-based memory system that functions relatively independent of the hippocampus, which is traditionally believed to subserve spatial or episodic-like memory functions.

The pars compacta also plays a role in temporal processing and is activated during time reproduction. Lesions in the pars compacta leads to temporal deficits. As of late, the pars compacta has been suspected of regulating the sleep-wake cycle, which is consistent with symptoms such as insomnia and REM sleep disturbances that are reported by patients with Parkinson's disease. Even so, partial dopamine deficits that do not affect motor control can lead to disturbances in the sleep-wake cycle, especially REM-like patterns of neural activity while awake, especially in the hippocampus.

Clinical significance

The substantia nigra is critical in the development of many diseases and syndromes, including parkinsonism and Parkinson's disease. There exist a study showing that high-frequency stimulation delivery to the left substantia nigra can induce transient acute depression symptoms.

Parkinson's disease

Substantia nigra with loss of cells and Lewy body pathology

Main article: Parkinson's disease

Parkinson's disease is a neurodegenerative disease characterized, in part, by the death of dopaminergic neurons in the SNpc. The major symptoms of Parkinson's disease include tremor, akinesia, bradykinesia, and stiffness. Other symptoms include disturbances to posture, fatigue, sleep abnormalities, and depressed mood.

The cause of death of dopaminergic neurons in the SNpc is unknown. However, some contributions to the unique susceptibility of dopaminergic neurons in the pars compacta have been identified. For one, dopaminergic neurons show abnormalities in mitochondrial complex 1, causing aggregation of alpha-synuclein; this can result in abnormal protein handling and neuron death. Secondly, dopaminergic neurons in the pars compacta contain less calbindin than other dopaminergic neurons. Calbindin is a protein involved in calcium ion transport within cells, and excess calcium in cells is toxic. The calbindin theory would explain the high cytotoxicity of Parkinson's in the substantia nigra compared to the ventral tegmental area. Regardless of the cause of neuronal death, the plasticity of the pars compacta is very robust; Parkinsonian symptoms do not generally appear until at least 30% of pars compacta dopaminergic neurons have died. Most of this plasticity occurs at the neurochemical level; dopamine transport systems are slowed, allowing dopamine to linger for longer periods of time in the chemical synapses in the striatum.

Menke, Jbabdi, Miller, Matthews and Zari (2010) used diffusion tensor imaging, as well as T1 mapping to assess volumetric differences in the SNpc and SNpr, in participants with Parkinson's compared to healthy individuals. These researchers found that participants with Parkinson's consistently had a smaller substantia nigra, specifically in the SNpr. Because the SNpr is connected to the posterior thalamus, ventral thalamus and specifically, the motor cortex, and because participants with Parkinson's disease report having a smaller SNprs (Menke, Jbabdi, Miller, Matthews and Zari, 2010), the small volume of this region may be responsible for motor impairments found in Parkinson's disease patients. This small volume may be responsible for weaker and/or less controlled motor movements, which may result in the tremors often experienced by those with Parkinson's.

Oxidative stress and oxidative damage in the SNpc are likely key drivers in the etiology of Parkinson’s disease as individuals age. DNA damages caused by oxidative stress can be repaired by processes modulated by alpha-synuclein. Alpha synuclein is expressed in the substantia nigra, but its DNA repair function appears to be compromised in Lewy body inclusion bearing neurons. This loss may trigger cell death.

Schizophrenia

See also: Dopamine hypothesis of schizophrenia

Increased levels of dopamine have long been implicated in the development of schizophrenia. However, much debate continues to this day surrounding this dopamine hypothesis of schizophrenia. Despite the controversy, dopamine antagonists remain a standard and successful treatment for schizophrenia. These antagonists include first generation (typical) antipsychotics such as butyrophenones, phenothiazines, and thioxanthenes. These drugs have largely been replaced by second-generation (atypical) antipsychotics such as clozapine and paliperidone. In general, these drugs do not act on dopamine-producing neurons themselves, but on the receptors on the post-synaptic neuron.

Other, non-pharmacological evidence in support of the dopamine hypothesis relating to the substantia nigra include structural changes in the pars compacta, such as reduction in synaptic terminal size. Other changes in the substantia nigra include increased expression of NMDA receptors in the substantia nigra, and reduced dysbindin expression. Increased NMDA receptors may point to the involvement of glutamate-dopamine interactions in schizophrenia. Dysbindin, which has been (controversially) linked to schizophrenia, may regulate dopamine release, and low expression of dysbindin in the substantia nigra may be important in schizophrenia etiology. Due to the changes to the substantia nigra in the schizophrenic brain, it may eventually be possible to use specific imaging techniques (such as neuromelanin-specific imaging) to detect physiological signs of schizophrenia in the substantia nigra.

Wooden Chest Syndrome

Wooden chest, also called fentanyl chest wall rigidity syndrome, is a rare side effect of synthetic opioids such as Fentanyl, Sulfentanil, Alfentanil, Remifentanil. It results in a generalised increase in skeletal muscle tone. The mechanism is thought to be via increased dopamine release and decreased GABA release in the nerves of the substantia nigra/striatum. The effect is most pronounced on the chest wall muscles and can lead to impaired ventilation. The condition is most commonly observed in anaesthesia where rapid and high doses of these drugs are given intravenously.

Multiple system atrophy

Multiple system atrophy characterized by neuronal degeneration in the striatum and substantia nigra was previously called striatonigral degeneration.

Chemical modification of the substantia nigra

Chemical manipulation and modification of the substantia nigra is important in the fields of neuropharmacology and toxicology. Various compounds such as levodopa and MPTP are used in the treatment and study of Parkinson's disease, and many other drugs have effects on the substantia nigra.

Amphetamine and trace amines

See also: Amphetamine and Trace amine

Studies have shown that, in certain brain regions, amphetamine and trace amines increase the concentrations of dopamine in the synaptic cleft, thereby heightening the response of the post-synaptic neuron. The various mechanisms by which amphetamine and trace amines affect dopamine concentrations have been studied extensively, and are known to involve both DAT and VMAT2. Amphetamine is similar in structure to dopamine and trace amines; as a consequence, it can enter the presynaptic neuron via DAT as well as by diffusing through the neural membrane directly. Upon entering the presynaptic neuron, amphetamine and trace amines activate TAAR1, which, through protein kinase signaling, induces dopamine efflux, phosphorylation-dependent DAT internalization, and non-competitive reuptake inhibition. Because of the similarity between amphetamine and trace amines, it is also a substrate for monoamine transporters; as a consequence, it (competitively) inhibits the reuptake of dopamine and other monoamines by competing with them for uptake, as well.

In addition, amphetamine and trace amines are substrates for the neuronal vesicular monoamine transporter, vesicular monoamine transporter 2 (VMAT2). When amphetamine is taken up by VMAT2, the vesicle releases (effluxes) dopamine molecules into the cytosol in exchange.

Cocaine

See also: Cocaine

Cocaine's mechanism of action in the human brain includes the inhibition of dopamine reuptake, which accounts for cocaine's addictive properties, as dopamine is the critical neurotransmitter for reward. However, cocaine is more active in the dopaminergic neurons of the ventral tegmental area than the substantia nigra. Cocaine administration increases metabolism in the substantia nigra, which can explain the altered motor function seen in cocaine-using subjects. The inhibition of dopamine reuptake by cocaine also inhibits the firing of spontaneous action potentials by the pars compacta. The mechanism by which cocaine inhibits dopamine reuptake involves its binding to the dopamine transporter protein. However, studies show that cocaine can also cause a decrease in DAT mRNA levels, most likely due to cocaine blocking dopamine receptors rather than direct interference with transcriptional or translational pathways.

Inactivation of the substantia nigra could prove to be a possible treatment for cocaine addiction. In a study of cocaine-dependent rats, inactivation of the substantia nigra via implanted cannulae greatly reduced cocaine addiction relapse.

Levodopa

See also: Levodopa

The substantia nigra is the target of chemical therapeutics for the treatment of Parkinson's disease. Levodopa (commonly referred to as L-DOPA), the dopamine precursor, is the most commonly prescribed medication for Parkinson's disease, despite controversy concerning the neurotoxicity of dopamine and L-DOPA. The drug is especially effective in treating patients in the early stages of Parkinson's, although it does lose its efficacy over time. Levodopa can cross the blood–brain barrier and increases dopamine levels in the substantia nigra, thus alleviating the symptoms of Parkinson's disease. The drawback of levodopa treatment is that it treats the symptoms of Parkinson's (low dopamine levels), rather than the cause (the death of dopaminergic neurons in the substantia nigra).

MPTP

See also: MPTP

MPTP, is a neurotoxin specific to dopaminergic cells in the brain, specifically in the substantia nigra. MPTP was brought to the spotlight in 1982 when heroin users in California displayed Parkinson's-like symptoms after using MPPP contaminated with MPTP. The patients, who were rigid and almost completely immobile, responded to levodopa treatment. No remission of the Parkinson's-like symptoms was reported, suggesting irreversible death of the dopaminergic neurons. The proposed mechanism of MPTP involves disruption of mitochondrial function, including disruption of metabolism and creation of free radicals.

Soon after, MPTP was tested in animal models for its efficacy in inducing Parkinson's disease (with success). MPTP induced akinesia, rigidity, and tremor in primates, and its neurotoxicity was found to be very specific to the substantia nigra pars compacta. In other animals, such as rodents, the induction of Parkinson's by MPTP is incomplete or requires much higher and frequent doses than in primates. Today, MPTP remains the most favored method to induce Parkinson's disease in animal models.

History

The substantia nigra was discovered in 1784 by Félix Vicq-d'Azyr, and Samuel Thomas von Sömmerring alluded to this structure in 1791. The differentiation between the substantia nigra pars reticulata and compacta was first proposed by Sano in 1910. In 1963, Oleh Hornykiewicz concluded from his observation that ‘‘cell loss in the substantia nigra (of Parkinson's disease patients) could well be the cause of the dopamine deficit in the striatum’’.